Abstract
We study the factorisation properties of one-loop scattering amplitudes in the triple collinear limit and extract the universal splitting amplitudes for processes initiated by a gluon. The splitting amplitudes are derived from the analytic Higgs plus four partons amplitudes. We present compact results for primitive helicity splitting amplitudes making use of super-symmetric decompositions. The universality of the collinear factorisation is checked numerically against the full colour six parton squared matrix elements.
Highlights
The ability to make finite predictions for important LHC observables
We study the factorisation properties of one-loop scattering amplitudes in the triple collinear limit and extract the universal splitting amplitudes for processes initiated by a gluon
We present compact results for primitive helicity splitting amplitudes making use of super-symmetric decompositions
Summary
A general QCD amplitude can be decomposed into a basis of SU(Nc) colour factors and ordered partial amplitudes which depend only on the momenta and helicities of the external legs. For cross-section computations we are required to square these amplitudes and sum over the colour indices. This sum can be represented as, M(nL,L )({pλi i }) = =. Partial amplitudes may in turn be written in terms of primitive amplitudes A[pX] which further decompose colour and flavour structure due to the internal loops, A(nL;c) =. In the limit where m of the external legs become simultaneously collinear, the amplitudes factorise into a product of lower multiplicity amplitudes and splitting amplitudes which contain all the infrared divergences: L. where A(nL) and Sp(nL) can either be primitive or partial n-point amplitudes and splitting amplitudes respectively, while and P ≡ p1 + · · · + pm. Sp(−P λP ; pλ11 , . . . , pλnn ) ≡ Spn(−P λP ; {pλi i }) A(pλ11 , . . . , pλnn ) ≡ An({pλi i })
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